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JEE • PHYSICS • UNITS & MEASUREMENTS

Units & measurements practice · Medium

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 502 questions

1 Medium

1 of 502

Analyzing +4 | -1

The method of dimensional analysis can be used to derive which of the following relations?

View answer and explanation

Correct option: D

None of the above

Option D (None of the above) is correct because dimensional analysis cannot be used to derive relations involving transcendental functions or sums of terms with different dimensions.

2 Medium

2 of 502

Remembering +4 | -1

The dimensions of torque are

View answer and explanation

Correct option: B

\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]

Option B (

\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]

) is correct because torque is force times distance, and its dimensions are mass times length squared times time to the power of -2.

3 Medium

3 of 502

Analyzing +4 | -1

The physical quantity having the dimensions

\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{A}^2}{T^3}} \right]

View answer and explanation

Correct option: C

Electrical conductivity

Option C is correct. The dimensions given correspond to electrical conductivity, which is the inverse of resistivity.

4 Medium

4 of 502

Analyzing +4 | -1

A quantity X is given by

{\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}},\;

, where

{\varepsilon _0}

is the permittivity of free space, L is a length,

{\Delta V}

is a potential difference and

{\Delta t}

is a time interval. The dimensional formula for X is the same as that of

View answer and explanation

Correct option: D

Electric current

Option D (Electric current) is correct because the given expression has the same dimensions as electric current.

5 Medium

5 of 502

Application +4 | -1

L = 2.331\;cm,\;B = 2.1\;cm,

then L+B=

View answer and explanation

Correct option: C

4.4 cm

Option C (4.4 cm) is correct because the sum of L and B, considering significant figures, is 4.4 cm.

6 Medium

6 of 502

Application +4 | -1

The density of wood is 0.5 in C.G.S system of units. The corresponding value in M.K.S unit is

View answer and explanation

Correct option: A

500

Option A (500) is correct because converting the density from C.G.S to M.K.S units results in 500 kg/m³.

7 Medium

7 of 502

Analyzing +4 | -1

Assertion: The equation

y=2 x+t

is physically incorrect if

x \,\&\, y

are distances and

t

is time.
Reason: Quantities with different dimensions cannot be added or subtracted.

View answer and explanation

Correct option: A

If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion

Option A is correct because the equation is dimensionally incorrect, and quantities with different dimensions cannot be added.

8 Medium

8 of 502

Analyzing +4 | -1

Given equation

\frac{1}{2} m v^2=m g h

, where

m

is the mass of the body,

v

is velocity,

g

is the acceleration due to gravity and

h

is the height. Then the given equation is

View answer and explanation

Correct option: B

Dimensionally correct

Option B (Dimensionally correct) is correct because both sides of the equation have the same dimensions (

ML^2T^{-2}

9 Medium

9 of 502

Understanding +4 | -1

Which of the following quantities is dimensionless

View answer and explanation

Correct option: D

None

Option D (None) is correct because Gravitational constant, Planck's constant, and Power of a convex lens all have dimensions.

10 Medium

10 of 502

Understanding +4 | -1

The dimensions of electric potential are

View answer and explanation

Correct option: A

\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}{\mathrm{Q}^{ - 1}}} \right]

Option A (

{\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}{\mathrm{Q}^{ - 1}}}

) is correct because it represents the dimensions of energy per unit charge, which is the definition of electric potential.

11 Medium

11 of 502

Analyzing +4 | -1

Of the following quantities, which one has the dimensions different from the remaining three?

View answer and explanation

Correct option: D

Angular momentum per unit mass

Option D (Angular momentum per unit mass) is correct because it has different dimensions compared to energy density, force per unit area, and the product of charge per unit volume and voltage.

12 Medium

12 of 502

Understanding +4 | -1

Which of the following is most precise measurement?

View answer and explanation

Correct option: D

0.0005 \mathrm{~m}

Option D (0.0005 m) is correct because the smaller the least count of a measuring instrument, the more precise the measurement.

13 Medium

13 of 502

Analyzing +4 | -1

The physical quantity which is not a unit of energy is

View answer and explanation

Correct option: B

MeV-sec

Option B (MeV-sec) is correct because it represents energy multiplied by time, not energy itself.

14 Medium

14 of 502

Understanding +4 | -1

Dimensions of bulk modulus are

View answer and explanation

Correct option: B

\left[ {\mathrm{M}{\mathrm{L}^{ - 1}}{\mathrm{T}^{ - 2}}} \right]

Option B

\left[ {\mathrm{M}{\mathrm{L}^{ - 1}}{\mathrm{T}^{ - 2}}} \right]

is correct because it represents the dimensions of bulk modulus, which is stress divided by strain.

15 Medium

15 of 502

Understanding +4 | -1

In the equation

y=a \sin (\omega t+k x)

, the dimensional formula of

\omega

View answer and explanation

Correct option: A

\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]

Option A ([M⁰ L⁰ T⁻¹]) is correct because the argument of the sine function must be dimensionless, so ωt has dimensions of 1, making ω have dimensions of T⁻¹.

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16 Medium

16 of 502

Application +4 | -1

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 %, the maximum error in determining the density is

View answer and explanation

Correct option: C

0.045

Option C (4.50%) is correct because it is the maximum error calculated using the formula for density and the given relative errors.

17 Medium

17 of 502

Understanding +4 | -1

Which of the following numerical values has three significant figures?

View answer and explanation

Correct option: D

0.300

Option D (

0.300

) is correct because trailing zeros after the decimal point are significant, giving it three significant figures.

18 Medium

18 of 502

Analyzing +4 | -1

Given that υ is speed, r is the radius and g is the acceleration due to gravity. Which of the following is dimensionless

View answer and explanation

Correct option: A

{\upsilon ^2}/rg

Option A (

{\upsilon ^2}/rg

) is correct because the expression is dimensionless, as it represents the square of speed divided by the product of radius and acceleration due to gravity, resulting in a dimensionless quantity.

19 Medium

19 of 502

Application +4 | -1

If P represents radiations pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, the non-zero integers x,y and z such that 

{P^x}{Q^y}{c^z}

is dimensionless, are

View answer and explanation

Correct option: B

x = 1,\;y = - 1,\;z = 1

Option B (

x = 1,\;y = - 1,\;z = 1

) is correct because it satisfies the dimensional analysis equation, making the expression dimensionless.

20 Medium

20 of 502

Analyzing +4 | -1

Velocity of object is given as a function of time and position.

v=\alpha t+\beta x+\gamma

then dimension of

\alpha, \beta

and

\gamma

are

View answer and explanation

Correct option: B

L T^{-2}, T^{-1}, L T^{-1}

Option B (

L T^{-2}, T^{-1}, L T^{-1}

) is correct because it correctly derives the dimensions of alpha, beta, and gamma by equating the dimensions of each term in the equation.

21 Medium

21 of 502

Remembering +4 | -1

The unit of Stefan's constant

\sigma

is:

View answer and explanation

Correct option: C

W m^{-2} K^{-4}

Option C (

W m^{-2} K^{-4}

) is correct because Stefan's constant relates the power radiated per unit area of a black body to the fourth power of its absolute temperature, and its unit is derived from the Stefan-Boltzmann law.

22 Medium

22 of 502

Application +4 | -1

The density of a material in CGS system of units is

4g/c{m^3}

, In a system of units which unit of length is 10 cm and unit of mass is 100 g , the value of density of material will be

View answer and explanation

Correct option: D

Option D (40) is correct because the density is transformed using the conversion factors for mass and length to the new system of units.

23 Medium

23 of 502

Application +4 | -1

The two full turns of circular scale of screw gauge cover a distance of

1 \mathrm{~mm}

on scale. The total division on circular scale is 50 further if found that screw gauge has a zero error of

-0.01 \mathrm{~mm}

. While measuring the diameter of thin wire a student notes the main scale reading of

2 \mathrm{~mm}

and the no of circular scale division in line with the main scale as 25. The diameter of wire is

View answer and explanation

Correct option: A

2.26 \mathrm{~mm}

Option A (

2.26 \mathrm{~mm}

) is correct because it is calculated using the formula for screw gauge reading, including zero error correction.

24 Medium

24 of 502

Application +4 | -1

The least count of a stop watch is 0.2 s. The time of 20 oscillations of a pendulum is measured to be 25 s. The percentage error in the measurement of time will be

View answer and explanation

Correct option: C

0.008

The correct answer is C (0.008). The percentage error is calculated by dividing the least count by the measured time and multiplying by 100.

25 Medium

25 of 502

Analyzing +4 | -1

Which of the following physical quantities represent the dimensions of

b / a

in the relation

P=\left(x^2-b\right) / a t

, where

P

is power,

x

is distance and '

t

' time?

View answer and explanation

Correct option: C

Torsional constant

Option C is correct because the dimensions of b/a are equivalent to the dimensions of the torsional constant.

26 Medium

26 of 502

Application +4 | -1

To determine the Young’s modulus of a wire, the formula is

Y = \frac{F}{A} \times \frac{L}{{\Delta L}}

; where L= length, A= area of cross-section of the wire,

{\Delta L}

= change in length of the wire when stretched with a force F. The conversion factor to change it from CGS to MKS system is

View answer and explanation

Correct option: C

0.1

Option C (0.1) is correct because the conversion factor from CGS to MKS for Young's modulus (dyne/cm²) to N/m² is 0.1.

27 Medium

27 of 502

Analyzing +4 | -1

Which of the following combinations have the dimensions of time?

L-C-R

represent inductance, capacitance and resistance, respectively.

View answer and explanation

Correct option: A

R C

Option A is correct because the product of resistance and capacitance (RC) has the dimensions of time.

28 Medium

28 of 502

Understanding +4 | -1

The dimensional representation of Planck's constant is identical to that of

View answer and explanation

Correct option: D

angular momentum

Option D (angular momentum) is correct because both Planck's constant and angular momentum have the same dimensional formula, which is ML²T⁻¹.

29 Medium

29 of 502

Analyzing +4 | -1

From the equation

\tan \theta = \frac{{rg}}{{{v^2}}},

one can obtain the angle of banking

\theta

for a cyclist taking a curve (the symbols have their usual meanings). Then say it is,

View answer and explanation

Correct option: C

Dimensionally correct only

Option C is correct because the equation is dimensionally correct, but numerically incorrect as the correct equation is

\tan \theta = \frac{v^2}{rg}

30 Medium

30 of 502

Application +4 | -1

If momentum

P,

area

A

and time

T

are taken to be the fundamental quantities, then the dimensional formula for energy is

View answer and explanation

Correct option: C

\left[ {P{A^{1/2}}\,\,{T^{ - 1}}} \right]

Option C (

\left[ {P{A^{1/2}}\,{T^{ - 1}}} \right]

) is correct because it is the derived dimensional formula for energy in terms of momentum, area, and time.

Revision notes and key takeaways

Review UNITS & MEASUREMENTS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 502 single-correct-answer MCQs on UNITS & MEASUREMENTS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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